Monetary policy and asset pricing - Assignment no.1

The Value function

The value function represents the preferences given the risk premium rate = ‘dummy’ and ‘x’ = risk-free rate as input returns a higher value when x -> 1 and dummy > 4. The symmetric hyperbolic gives the function that evaluates the proximity to 1 of the risk-free rate function: \[ y=\frac{1}{|1-x|} \] While a dummy variable represents the risk-premium rate condition: \[ f(n) = \begin{cases} 1, & \mbox{if } risk premium\mbox{ <5\%} \\ 2, & \mbox{otherwise } \end{cases} \] Finally, the value function can be represented as: \[ g(n) = ln(\frac{1}{|1-x|}*f(n)) \]

library(plotly)

## Loading required package: ggplot2

## 
## Attaching package: 'plotly'

## The following object is masked from 'package:ggplot2':
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##     last_plot

## The following object is masked from 'package:stats':
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##     filter

## The following object is masked from 'package:graphics':
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v <- function(dummy, x) {
  # value function: given the risk premium rate = 'dummy' and
  # 'x' = risk free rate as input return a value which is higher
  # when x -> 1 and  dummy > 4

  for (t in seq_along(dummy)) {
    if (dummy[t] > 4) {
      dummy[t]  <-  2
    }
    else {
      dummy[t]  <-  1
    }
  }
  value <-  log(abs(1 / (1 - x)) * dummy)
  return(value)
}
graphValueFunction  <-  function(){
  risk_prem <-  c(seq(2, 6, 0.02))
  risk_free <-  c(seq(0.01, 2, 0.01))
  value     <- matrix(0, nrow = 0, ncol = 3)
  for (x in risk_prem) {
    for(y in risk_free){
      value  <-  rbind(value, c(log(v(x, y)), x, y))
    }
     
  }
  value[!is.finite(value[, 1]), 1] <- 0
  plot_ly(z = value, type = "surface")
}
graphValueFunction()